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Check your understanding 36. Suppose we want to set up a triple integral over the region defined by the inequalities x2 ≤ y ≤ 1 and 0 ≤ z ≤ 1 − y in the order dx dy dz. What are the z limits? (a) 0 ≤ z ≤ 1. (b) 0 ≤ z ≤ 1 − y. (c) 0 ≤ z ≤ 0. (d) −∞ < z ≤ 1. Answer: (a). Explanation: We are given that 0 ≤ z ≤ 1 − y. Since y ≥ x2, we must have y ≥ 0, so 1 − y ≤ 1. Note that (b) does not make sense because y is not fixed. The answer can only involve constants.